Updated at 8:26 p.m. ET
Though life-threatening flooding still poses a threat to Louisiana, weakening winds on Sunday marked Barry's downgrade from a tropical storm to a tropical depression.
The National Weather Service forecasts that the center of the storm will continue to move through northwest Louisiana toward Arkansas through Monday.
Barry began losing steam when it touched down on the Louisiana coast on Saturday. Still, the National Weather Service warns of ongoing dangers posed by storm surges and the possibility of tornadoes in areas including parts of Louisiana and Mississippi.
Louisiana Gov. John Bel Edwards said Sunday evening that he's "extremely grateful" that Tropical Depression Barry didn't cause the devastating floods that had been projected.
There were no weather-related fatalities, he said.
Search teams rescued 93 people from 11 parishes, Edwards said.
"This storm still has a long way to go before it leaves the state," Edwards said on Saturday night. "We still have a significant amount of rain coming our way.
Forecasters say rainfall estimates over south-central Louisiana now stand around 3 to 5 inches, with isolated maximum rainfall reaching as much as 15 inches, causing the potential for dangerous flooding.
Barry was briefly a Category 1 hurricane but the system weakened to a tropical storm. And on Sunday, maximum sustained winds decreased to 35 miles per hour with higher gusts.
With the slow-moving system carrying such heavy downpours into the saturated ground and along rivers and streams already at high levels, Louisiana Gov. Edwards said on Saturday night that it was not the time for residents to act like they are out of the woods just yet.
"Some people may think that the threat is over. Some people may be tempted to think that because it was a Category 1 when it came ashore and has already been downgraded to a tropical storm, that it does not present a threat," Edwards said. "That is not the case."
As Barry moved inland on Saturday, water was spilling over levees in Terrebonne and Plaquemines parishes, according to AccuWeather, which has been tracking the storm.
A mandatory evacuations for areas along Louisiana Highway 315 was cancelled on Sunday morning.
Gov. Edwards said Saturday night that levees overtopping have been addressed and are no longer a concern.
More than 70,000 customers in Louisiana remained without power Sunday evening, according to poweroutage.us. Many businesses remain closed, air travel experienced delays and conventions planned in the area have been cut short. The Coast Guard closed the Mississippi River to shipping traffic.
The storm is also impacting America's energy industry. About 300 offshore oil and gas rigs and platforms have been evacuated, resulting in a 70% drop in oil production and the amount of natural gas usually produced in the Gulf has been cut in half, according to Bureau of Safety and Environmental Enforcement.
As the storm moved north, officials at the Louis Armstrong New Orleans International Airport announced Sunday that most airlines are resuming normal operations. "If you have travel scheduled today, check with your airlines directly for the most accurate info. Arrive 2+ hours early as we may see long lines," airport officials said.
Louisiana's National Guard had some 3,000 soldiers deployed around the state. And Coast Guard helicopters have conducted rescues, as people on Saturday sought safety on rooftops and other high places as downpours pounded the area.
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